On Tue, 1 Jun 2004 15:25:44 +0000 (UTC), 
Tim Tyler  wrote:
> Larry Moran  wrote or quoted:
> 
>> The question you didn't ask is what percentage of mutations have
>> selection coefficients that are large enough to ensure fixation in
>> reasonable-sized populations.
> 
> In my example, the mutants were *deleterious*.  Selection prevented
> their fixation by genetic drift.  The alleles weren't fixed by
> selection - they were prevented (by selection) from reaching fixation
> (by genetic drift).

In other words, the other, beneficial, allele was selected over the
deleterious allele.

> The question of how many mutations are sufficiently deleterious to be 
> affected in this way in realistic populations is an interesting one
> - but some are bound to be, and that seems sufficient to establish that 
> the chance of alleles getting fixed by genetic drift can be a function 
> of the size of the population.

The probability of a *particular* allele becoming fixed by random genetic 
drift (alone) is
                          1
                     P = ---
                         2N

where N is the population size. This means that the probability for each
allele depends on the population size. This isn't disputed. The probability 
of *any* allele becoming fixed in a population by drift is the probability 
of fixing each allele times the number of alleles that arise by mutation. 
The number of alleles that arise in a population is given by 2Nu where
u is the rate of mutation (per gene per generation).

Thus, the rate of substitution of neutral alleles in a population is

                                1 
                     K = 2Nu x --- = u
                               2N

and it is independant of population size.

For beneficial alleles that arise in a population the probability of
fixation can be approximated by 

                     P = 2s

where s is the selective advantage. This equation holds for small values of
s (s < 0.05) and populations greater than about 100 individuals. It is pretty 
much independant of population size for realistic populations. For a
population of 100 and a selective advantage of 0.001 the equation yields
a probability of 0.002 (0.2%) and this is only a bit higher than the 
probability (1/2N = 0.005) that the allele would be fixed by drift alone
it it were neutral. As the selective advantage goes even lower (i.e.
very close to neutral) the probability of fixation by natural selection
falls below the probabilty of fixation by drift.

Your simulations were a bit unrealistic since you started with equal numbers 
of deleterious and benefical alleles (50:50) and very small populations. 
You didn't explain how a deleterious mutation rose to the level of 50%
in your populations.

>> You also need to ask whether there's any evidence that the nucleotide 
>> substitutions we see in most DNA could possibly be slightly 
>> advantageous or slightly deleterious.
> 
> Nucleotide substitutions that seem close to neutrality can nontheless 
> have effects on the phenotype in several ways.
> 
> For example, substitutions in junk DNA can be expressed by removing
> stop codons.
> 
> Similarly, "third-base" mutations can have effects even if they
> result in the same amino acid being coded for - since they can
> alter the probabilities of the sequence mutating into the
> sequences representing other amino acids.
> 
> Some viruses use enzymes to target particular DNA sequences - to
> identify where to paste themselves.  While such enzymes exist the
> exact details of the DNA sequence are likely to have selective
> consequences.
> 
> In other words, neutrality is an ideal which is not realised
> in practice - practically all alleles have some non-zero selection
> coefficient associated with them.

All of these hypothetical examples are situations where a neutral allele
isn't a neutral allele. You'll get no argument from me on this point.
There certainly are alleles that have low selective advantages and 
are affected by natural selection in competition with random genetic 
drift. On the other hand, there are lots of mutations in junk DNA that
aren't likely to have any effect on the organism. I conclude that 
that there are thousand and thousands of truly neutral alleles that 
have become fixed in the human population over time.

We began this discussion when I said that random genetic drift is the
main mechanism of evolution when you take into account *all* of evolution.
So far you haven't given me any definition of *all of evolution* that
causes me to change my mind. Right now you seem to be trying to deny that
there are any such thing as neutral mutations - even in junk DNA. Is
that how you intend to continue the discussion? Are you saying that random
genetic drift isn't the main mechanism of evolution because (almost) all
mutations are either beneficial or deleterious?





Larry Moran
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